Bulk Material Belt Conveyor Calculator (ISO 5048)

Capacity and belt fill

The material sits in the trough formed by three equal idler rolls. ISO 5048 splits its cross-section into a trough part S₂ (below the line joining the material edges) and a surcharge part S₁ (a heap whose slope is the surcharge angle θ). Only a usable width b = 0.9 B − 0.05 is loaded, to keep the edges clean.

Q_max = 3600 × S × v × ρ × k

On an incline the heap flattens, so the slope factor k reduces the surcharge part. If the incline reaches the surcharge angle, the surcharge part is lost. Belt fill is the required capacity as a share of Q_max; aim for 85 % or less to avoid spillage.

What C and f mean

The friction factor f covers the main resistances along the conveyor: idler rotation, belt flexing over the idlers and the material being kneaded as it passes each idler. The length coefficient C adds the secondary resistances that do not grow with length, such as loading the material, belt cleaners and pulley bearings, so C is large for short conveyors and close to 1 for long ones.

F_U = C f L g [m_R + (2 m_B + m_G) cosδ] + H g m_G

Why T₂ is set by slip or sag

The drive pulley can only pass the effective tension to the belt if the slack side has enough tension, by Euler's belt friction: T₁ / T₂ ≤ e^μα. At start-up the drive pulls k_A × F_U, so T₂ must stop slip then. The belt must also not sag too much between idlers, mostly at the tail where the tension is lowest. T₂ is the largest of these needs, and the take-up applies it.

When a backstop is needed

On an incline the material wants to run back when the conveyor stops. If the lift resistance is more than about half of the friction resistance, friction alone will not hold the loaded belt, so a backstop (holdback) is needed on the drive.

This is a preliminary sizing method. Long, high powered, curved or declined conveyors need a full ISO 5048 or CEMA design with dynamic start and stop analysis. Confirm belt, idler and pulley selections with the suppliers.

Basic / Advanced

Basic uses the recommended defaults: f = 0.020, start-up factor 1.5, 1 % sag, belt safety factor 10, gearbox efficiency 0.95, service factor 1.1, and belt and idler masses estimated from the belt width. Advanced lets you enter your own values.

Material values

Bulk density, surcharge angle, maximum incline and maximum belt speed are typical values. Confirm them for your material, because moisture and lump size change them.

Belt width, trough angle, speed

A wider belt, a deeper trough or a faster belt carries more. Narrow belts should not run faster than about 2 m/s.

Length and lift

L is measured along the belt between pulley centres. H is the lift from tail to head; it must be 0 or positive because declines are outside the scope of this calculator.

Friction factor f

0.017 for a well aligned and maintained conveyor, 0.020 for normal conditions, 0.023 to 0.030 for poor alignment, cold or dirty conditions.

Start-up factor kA

The peak drive force at start-up compared with running. VFD or soft starter 1.2 to 1.3, fluid coupling 1.3 to 1.5, direct on line (DOL) 1.8 to 2.2.

Pulley friction μ and wrap α

Lagging and a larger wrap angle let the pulley drive with less slack side tension. Rubber lagged 0.35, ceramic 0.40, bare steel 0.25 dry or 0.10 wet.

Belt safety factor and rating

The belt rating needed is T₁ × S / B. A safety factor of about 10 suits textile EP belts; the belt supplier may need a heavier carcass for impact, load support and troughing.

Lump size

The belt width should be at least 3 times the largest lump for mixed material, or 5 times if all lumps are the same size.

Motor poles, Auto

Auto picks a 4 pole motor (1440 rpm at 50 Hz, 1740 rpm at 60 Hz) when the gearbox ratio is between 5 and 150. If the ratio would be above 150 it steps to a 6 or 8 pole motor. A ratio below 5 needs a larger drive diameter or a low-ratio gearbox, because a slower motor would lower the ratio further. 2 pole motors are never picked automatically.

Custom motor

Enter the nameplate speed and power of an existing motor. It passes when its rated power covers the required power times the service factor, is marginal when it only covers the required power, and is undersized below that.

Motor supply: DOL or VFD

DOL (direct on line) runs the motor straight from the supply at full speed. A VFD (variable frequency drive, also called an inverter or VSD) changes the motor speed by changing the frequency, so the conveyor speed changes in proportion; the design frequency is where it runs at the set speed. Self-cooled motors need derating below about 25 Hz. The 87 Hz switch (104 Hz at 60 Hz) runs a 230/400 V motor in delta for about 1.73 times the power, so a smaller motor and a higher gearbox ratio.

Abbreviations

IEC: International Electrotechnical Commission, whose standard motor sizes (0.18 to 22 kW here) are used for the recommended motor. DOL: direct on line. VFD: variable frequency drive. PWM: pulse width modulation, the fast voltage pulses a VFD uses to build its output. SF: service factor. μ: friction or rolling resistance coefficient. rpm: revolutions per minute.